Abstract
We consider a stochastic version of a system of two equations formulated by Burgers [Burgers, J.M. Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion. Verh. Kon. Nerderl. Akad. Weten-Schappen Amsterdam, Afdeel Natuurkunde, 1939, 17 (2), 1–53] with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness theorem for a global solution is established. The paper generalizes the result from the paper by Da Prato and Ga¸tarek [Da Prato, G.; Ga¸tarek, D. Stochastic Burgers equation with correlated noise. Stochastics Stochastics Rep. 1995, 52, 29–41] dealing with the equation describing only the turbulent motion.
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